Jada has a stand in the marketplace where she sells ground cumin. Her weekly expenses are $\$300$, and she sells her cumin at a fixed price per kilogram. If she sells $120$ kilograms of cumin, her weekly net profit is $\$600$. What is the price of a kilogram of Jada's cumin? $\$$
Explanation: Let's say that each kilogram of cumin costs $C$ dollars. Then, $W$ kilograms of cumin cost $W\cdot C$ dollars. In addition, we know that Jada's weekly expenses are $\$300$. Jada's weekly net profit is found by taking her income from selling cumin and subtracting her weekly expenses. We can express this with the equation $P=W\cdot C-300$, where: $P$ represents Jada's weekly net profit (in dollars) $W$ represents the amount of cumin she sold (in kilograms) $C$ represents the price of $1$ kilogram of cumin (in dollars) We know that if Jada sells $120$ kilograms of cumin $(W={120})$, her weekly net profit is $\$600$ $(P={600})$. Let's plug these values into the equation to find the value of $C$. $ \begin{aligned}{600}&={120}\cdot C-300\\ 120C&=900\\ C&=7.5\end{aligned}$ Therefore, each kilogram of Jada's cumin costs $\$7.50$. To find how much cumin Jada has to sell to cover her weekly expenses, we can plug $P=0$ into the equation and solve for $W$. $ \begin{aligned}0&=W\cdot7.5-300\\ 7.5W&=300\\ W&=40\end{aligned}$ Each kilogram of Jada's cumin costs $\$7.50$. Jada has to sell $40$ kilograms of cumin to cover her weekly expenses.